Question 5 solve the following system of equations by using the substitution method. y = 6x – 11 -2x – 3y = -7 (1, 2) (2, 1) (-3, 1) (2, 4)

answer is (2,1)

y = 6x – 11

-2x – 3y = -7

Substitute 6x - 11 for y in the second equation

-2x – 3(6x-11) = -7

-2x – 18x +33 = -7

-20x + 33 = -7

Now subtract 33 on both sides

-20x   = -7 - 33

-20x = -40 ( divide by -20 on both sides)

x= 2

We know y = 6x -11

Plug in 2 for x  and find out y

y = 6(2) -11= 12 -11 = 1

So answer is (2,1)

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet